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# 3 different ways to calculate the area in a triangle.

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Hi!

So I was doing an assignment and out of nowhere a question turned up that connfused me a bit.

The question is: Name 3 different ways to calculate the triangles area. The triangle is an perpendicular triangle. (A triangle with one corner that is 90 degrees)

The obvious one is of course B*H/2

The second one I'm thinking of is (a*b*sinC)/2 but I'm unsure if that one works on perpendicular triangles.

The third one I have no clue about. Anyone got any idea? =)

Guest Jun 8, 2017
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Let  sides  a,b  be the legs  and c the hypotenuse

Three possibilities

1st  way  =   product of the legs / 2

2nd way =    (1/2) (a)(c)sin B

Where B is the included angle between sides a and c

Also.....     (1/2) (b) (c) sin A    would work, too

3rd  way.....something known as "Heron's" Formula

The area, A, is given by

√ [  s (s - a) (s - b) ( s - c) ]

Where  s  = the semi-perimeter =   [ a + b + c ] / 2

CPhill  Jun 8, 2017